Chapter IV 

 MAYA ARITHMETIC 



The present chapter will be devoted to the consideration of Maya 

 arithmetic in its relation to the calendar. It will be shown how the 

 Maya expressed their numbers and how they used their several time 

 periods. In short, their arithmetical processes will be explained, 

 and the calculations resulting from their application to the calendar 

 will be set forth. 



The Maya had two different ways of writing their numerals,^ namely: 

 (1) With normal forms, and (2) with head variants ; that is, each of the 

 numerals up to and including 19 had two distinct characters which stood 

 for it, just as in the case of the time periods and more rarely, the days 

 and months. The normal forms of the numerals may be compared to 

 our Roman figures, since they are built up by the combination of 

 certain elements which had a fixed numerical value, like the letters 

 I, V, X, L, C, D, and M, which in Roman notation stand for the 

 values 1, 5, 10, 50, 100, 500, and 1,000, respectively. The head- 

 variant numerals, on the other hand, more closely resemble our 

 Arabic figures, since there was a special head form for each niunber 

 up to and including 13, just as there are special characters for the 

 first nine figures and zero in Arabic notation. Moreover, this 

 parallel between our Arabic figures and the Maya head-variant nu- 

 merals extends to the formation of the higher numbers. Thus, the 

 Maya formed the head-variant numerals for 14, 15, 16, 17, 18, and 

 19 by applying the essential characteristic of the head variant for 10 

 to the head variants for 4, 5, 6, 7, 8, and 9, respectively, just as the 

 sign for 10 — that is, one in the tens place and zero in the units place — 

 is used in connection with the signs for the first nme figm-es in Arabic 

 notation to form the numbers 11 to 19, inclusive. Both of these 

 notations occur in the inscriptions, but with very few exceptions ^ no 

 head-variant numerals have yet been found in the codices. 



Bar and Dot Numerals 



The Maya "Roman numerals " — that is, the normal-form numerals, 

 up to and including 19 — were expressed by varying combinations of 

 two elements, the dot (• ), which represented the numeral, or nmneri- 

 cal value, 1, and the bar, or line (^^^^H), which represented the nu- 

 meral, or numerical value, 5. By various combinations of these two 



1 The word "numeral," as used here, has been restricted to the first twenty numbers, to 19, inclu- 

 sive. 



2 See p. 96, footnote 1. 



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